a If a single glucose measurement is made what is the probab

(a) If a single glucose measurement is made, what is the probability that Sheila is diagnosed as having gestational diabetes?

(b) If measurements are made on 4 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Sheila is diagnosed as having gestational diabetes?

Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    140      
u = mean =    122      
          
s = standard deviation =    12      
          
Thus,          
          
z = (x - u) / s =    1.5      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.5   ) =    0.066807201 [ANSWER]

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b)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    140      
u = mean =    122      
n = sample size =    4      
s = standard deviation =    12      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    3      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   3   ) =    0.001349898 [ANSWER]